This will be remembered as the day Mario Balotelli announced his arrival in the Premier League and his new audience stared back with a glazed expression of shock and awe. Balotelli's first two goals in English football had therapeutic qualities for Manchester City, who will like to believe they have answered a few questions about their spirit of togetherness, but then we saw the other side of this gifted but temperamental striker.

Balotelli had already been shown a yellow card for dissent by the time he was sent off just after the hour, with a straight red, for kicking out at Youssouf Mulumbu as they tangled for the ball. Roberto Mancini argued that it was unjust and said the club would appeal but City's manager made little effort to conceal his disgust with his player, remonstrating with him on the touchline.

Mancini had already left the dug-out more than once to warn Balotelli to maintain his discipline, with the £24m signing from Internazionale apparently hell-bent on showing his more unappealing tendencies, whether it be picking fights with his opponents, arguing with the officials or a preposterous dive to try to win a penalty.

It was a pity he should have felt any of this was necessary because, after City had lost their last three matches, Balotelli's first‑half goals will go a long way to soothing any sense of crisis enveloping the most expensively assembled squad in the sport. A knee injury has disrupted his progress since signing in August but here was a demonstration of the penetration he can bring to a football club that is willing to put up with his behavioural flaws and, in the process, he will have done Mancini the world of good, given the pressure that had been building on the manager. Unfortunately for City the player's body language for much of the afternoon was of someone spoiling for a fight.

"I don't agree with the referee but I'm angry [with Balotelli] because I had explained to him he must pay attention with the referee," Mancini said. "I was trying to make a change to stop him getting a red card. I wanted to change Balotelli for Adam Johnson but I didn't have time."

Mancini's frustration was understandable – Balotelli will, in theory, be suspended from the Manchester derby on Wednesday plus the following league games against Birmingham City and Fulham and an appeal could see another game added if it is deemed frivolous – but this was otherwise a satisfying day for a manager whose position has come under scrutiny in certain quarters.

City's travelling fans repeatedly sang Mancini's name and the Italian responded at the end by walking across the pitch to acclaim them. "I must say thank you," he said. "When you lose two or three games the atmosphere [at the club] is not good but we played a fantastic game today."

All of which made Balotelli's hotheadedness even more unnecessary. His behaviour could also have had ramifications for Mancini's team coming at a point in the match when Albion were threatening to get back into it. As it was, City defended stoutly, with Vincent Kompany outstanding, and any hopes of a late comeback were effectively extinguished nine minutes from the end when Mulumbu was sent off for his second bookable offence, scything through the back of Carlos Tevez's legs.

Balotelli's more attractive side could be seen in the way he opened the scoring, turning in a low cross from Tevez at the far post. Balotelli, showing great upper-body strength, then held off Gabriel Tamas to control David Silva's through-ball and score the second with a shot on the turn from just inside the penalty area.

The goals came within seven minutes of one another midway through a first half in which City played with a confidence that might not have been expected from a side on a losing run. The fit-again Tevez made a big difference, Silva played with intelligence and Yaya Touré had possibly his finest game since his summer move from Barcelona.

There was a spirited response from the home side after the interval. Simon Cox drove a 30-yard shot against the post and Silva turned the ball against his own crossbar during one spell of penalty-area pressure. Even so City looked a constant menace on the counter-attack.

"It was a difficult afternoon," Roberto Di Matteo, the home manager, said. "They [City] were very good and we must give credit to them. We played against a great team today."